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Assignment 5: Exponential growth and mortality/Secondary production

Assignment 5: Exponential growth and mortality/Secondary production.

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Assignment 5: Exponential growth and mortality/Secondary production

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  1. Assignment 5: Exponential growth and mortality/Secondary production 1.) 180 pike were caught at random in a 30 ha lake and tagged. Two weeks later 200 more pike were captured and 40 of these were recaptured tagged fish. Estimate the total population of pike in this lake, assuming that all fish from both samples were caught in the same manner and that no mortality occurred in time between the samples and all fish caught were released unharmed. Explain your reasoning. 2.) The fish that were caught were weighed and measured before being released. The following data were obtained. All fish were caught during spring after the spawning period, before any young of the year had hatched. Assume that the age structure reflects the survivorship curve of the population, and using your population estimate from question 1 graph the number of fish in each age class vs age. Now calculate the mortality exponent for each age class, assuming an exponential function, and plot the mortality exponent vs age. Fit a trendline to this graph using the type of function that you think best fits the data, and extrapolate the function to the y-intercept to estimate the mortality exponent for the 0+ age class. Use this to estimate the number of newborn fish that will enter the population that year.

  2. 3. From the data presented above, calculate the biomass of pike in each age class (graph this data, biomass vs age), and calculate the total biomass of pike in the lake in kg/ha. What is the average size of a pike in this lake before the new cohort of fish hatch? 4.) Calculate the specific growth rate of biomass in each age class from the growth curve, using the assumption of exponential growth. Now calculate the productivity (biomass gained per year) of each age class (1-14) and compare it to biomass lost each year through mortality. Calculate the productivity averaged over all age classes weighted for the biomass of the age class.

  3. 5.) In our calculation of productivity for each age class we have ignored the fact that fish lose a lot of their accumulated weight at spawning time. Mature pike lose about 15% of their body weight in gametes and weight loss through activity. Pike spawn in early spring before fish biologists usually can get out and sample them, and if we assume that each of the spawning age classes would have been 15% heavier before spawning, we can correct our estimates of specific growth rate for this. How much of the population’s overall productivity was consumed in spawning? 6) Assume that the pike is the only fish in the lake at the fourth trophic level. How close is the productivity (kg/ha/yr) to what we would expect on the basis of the lake’s primary productivity if the lakes NPP is 500 g/m2/yr. Assume that each trophic level is 10% efficient at consuming and converting biomass from its resource base. If you assume that the biomass of the pike’s prey population (usually minnows, perch or suckers) is twice that of the pike population, what would you expect its specific growth rate to be.

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